Sunday, October 26, 2008

Tiger Woods: a bad golfer!

Nearly everyone thinks that Tiger Woods is an exceptional golfer. If you look at the statistics you will be surprised to see that Tiger Woods is an absolutely terrible player when you look at his performance in bunkers. It appears like a contradiction to have one of the best golfers in history to practically fail in certain aspects of the sport. How can one resolve this?
When looking at the performance of athletes or business professionals one oftentimes focuses on a dualistic view, i.e. one is good or bad at something. If you are bad at something then it follows that you should improve and become good at it. A lot of resources are put into place to advance and over time eventually one moves towards becoming "good at it". And so it goes.
The real question, however is, if the property is also "important". Maybe it is just "unimportant". What does that mean? In the example with Tiger Woods one can see by looking at the PGA statistics board that the "Tiger" is bad at bunker shots. However, if you add the second dimension of "Important/Unimportant" one can grasp to understand that this is a rather unimportant skills for Tiger. Why? Quite frankly, Tiger Woods can afford to be bad at bunker shots because he doesn't need to be good at bunker shots. Tiger Woods avoids hitting bunkers altogether therefore he doesn't need to waste his time improving his bad score but rather invests his scares resource, i.e. time, in further improving his performance on the green. The following 2x2 matrix illustrates this finding:
It is obvious to avoid activities on the left side and redirect resources and efforts from points "A" and "B" towards "T".  The not so obvious point is "how" to do this. Depending on the type of the "game" played or the business situation you are in, a solution will be different. In a "looser-game" (see details in my other blog postings) one will likely have to improve the position in "B" and move towards point "T". In a "Winner-game" you have the opportunity to abandon points "A" and "B" and concentrate on improving "T". This is what Tiger Woods does! Professional Golf (unlike amateur golf!) is a Winner-Game and the statistics prove that TW is improving on "T" while abondoning the bunker quadrant. 
A corporate citizen is often confronted with a Looser-Game unlike Entrepreneurs that are more likely to be participants in a Winner-Game. This might be the reason why large corporatins accumulate many mediocre players over time while top-performers will be playing in a different game.



Moving parts & lateral brain teaser


A lateral brain teaser is a question that cannot be solved with regular logic. Here is an example:

A sun dial is the time piece with the fewest moving parts. What is the time piece with the most moving parts? Answer: an hour glass is the most common answer. I personally think that Foucault pendulum is a good answer too since the whole apparatus moves. Granted it has less parts than an hour glass.

Saturday, October 25, 2008

First mover advantage

You and I play a game where we take turns rolling a die. I win if I roll a 4. You win if you roll a 5. If I go first, what’s the probability that I win? There are several answer options but I find the one below most intuitive:
This dice problem is mentally tricky because many rounds end without a winner. It would seem necessary to keep track of an infinite series to arrive at an answer. But that’s not the case. The trick is seeing that each round is really an independent sub-game. The fact that the previous round ended without a winner does not affect the winner of the current round or any future round. This means we can safely ignore outcomes without winners.

The probability of winning depends only on the features of a single round. This simplifies the problem to a more tractable one. So now, assume that one of the players did win in a round, and then calculate the relative winning percentages. In other words, calculate the probability the first player wins given the round definitely produced a winner. To do that, we look at the distribution of outcomes. In any given round, the first player can roll six outcomes, as can the second player. How many of those thirty-six outcomes produce a winner, and how many are from the first player?

This diagram illustrates the answer:

There are exactly 11 outcomes where somebody wins, of which 6 belong to the first player. Therefore, the first player wins with a 6/11 chance, or about 54.5 percent of the time. This is the same numerical answer as Monte Carlo, but we get an explanation why it works. The first-mover advantage is caused by the fact the first player wins even if both were to roll winning numbers.

Source: http://mindyourdecisions.com